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∫(sinx)/(sin4x) dx =∫1/4cosxcos2x dx =1/4 ∫cosx dx /cos2xcos2x ==1/4 ∫cosx dx /(1-sin2x)(1-2sin2x) let sinx =t cosx dx =dt =1/4 ∫dt /(1-t2)(1-2t2) use partial fraction =-1/4 ∫dt /(1-t2) + 1/8 ∫dt /(1-2t2) now onwards it is easily calculated
∫(sinx)/(sin4x) dx
=∫1/4cosxcos2x dx
=1/4 ∫cosx dx /cos2xcos2x
==1/4 ∫cosx dx /(1-sin2x)(1-2sin2x)
let sinx =t
cosx dx =dt
=1/4 ∫dt /(1-t2)(1-2t2)
use partial fraction
=-1/4 ∫dt /(1-t2) + 1/8 ∫dt /(1-2t2)
now onwards it is easily calculated
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